1. Field of the Invention
This invention relates to narrow band-pass tuned resonator filter topologies for advantageous application over high frequency (HF), very high frequency (VHF), ultra high frequency (UHF) and microwave bands, and more specifically to such topologies capable of maintaining over the frequency ranges of interest a high loaded Q for increased selectivity, optimal coupling to minimize insertion loss with improved out-of-band rejection, and which are relatively simple and inexpensive to manufacture with a high degree of repeatable accuracy.
2. Background of the Related Art
The processing of broadband multi-carrier signals presents a particularly rigorous and stringent context for signal processing circuitry such as filters. The base-band television signal for example, which has a bandwidth on the order of about 5-6 MHz, is typically mixed with (to modulate) an RF (radio frequency) carrier signal, thereby placing it on an RF channel in the range of 50 to 1000 MHz or greater, to achieve frequency division multiplexing (FDM). Other applications, such as in microwave communications, can require a range of operation of 1-2 GHz and beyond. Applications that require the processing of broadband signals containing a multiplicity of channels simultaneously, such as the transmission and reception of a television broadcast (either through air or via fiber optic/coaxial cable), can present situations requiring filters to pass only a small fraction of the total bandwidth (i.e. those frequencies that fall within the narrow pass band, typically one channel of interest) while rejecting the rest of the frequencies over the total bandwidth (i.e. those falling within the stop-band). This is typically accomplished using a narrow band-pass filter. Depending on the system design for a particular implementation, these filters may be required to operate on the same RF frequency as the RF channel of interest, or at some other frequency to which the RF channel may have been up or down converted (the intermediate frequency or IF), which is typical for wide frequency agile systems.
Noise and image signals, as well as various undesired spurious signals, can be injected or generated at various points in processing, and thus band-pass filters are often called upon to reject (i.e. attenuate) out-of-band signals to significantly low levels, depending upon the sensitivity of the application. For example, even signals attenuated up to 60 dB can still be seen in received video transmissions. Thus, it is often critically important that any signals present other than the base-band signal modulated on the desired carrier be sufficiently attenuated. This often requires band-pass filters to be very selective (i.e. ideally passing only that fraction of the total bandwidth that contains the base-band signal of interest), with little or no loss of energy in the pass-band (i.e. low insertion loss), but maintaining the requisite measure of attenuation for all other frequencies in the stop-band. Moreover, because the fraction of the total bandwidth occupied by base band signals in broadband applications are so small relatively speaking (on the order of 1-2%), such filters must produce the requisite frequency response with a high degree of accuracy and must maintain that response over time (i.e. the response should not drift). Further, they must be relatively immune to RF noise from external sources, as well as from coupling between their own components. Finally, it is always desirable that the filters be inexpensive, and easy to manufacture with a high degree of repeatable accuracy.
There are several known techniques for implementing band-pass filters. As previously discussed, the Q value of a filter indicates its selectivity; a filter's selectivity is defined by how quickly the filter's response transitions from the pass band to the stop band. The higher the Q of a filter, the steeper the roll-off from pass band frequencies to stop band frequencies. Because the input and output loading of a filter affects its Q, a more useful and practical measure is its “in-circuit” or loaded Q (i.e. QL). The QL of a filter is roughly equal to the reciprocal of the fractional bandwidth of its frequency response, which is typically measured between the points on the response curve that are 3 dB below the peak of the response (i.e. the half-power points of the response). Thus, the QL of a filter passing a 1-% fractional bandwidth is roughly 100. Narrow band-pass filters for broadband signal processing applications often require a high value of QL, while exhibiting low insertion loss (i.e. the amplitude of signals in the pass band should not be significantly attenuated), and attenuation off signals in the stop-band should meet the requirements of the applications.
One known technique for implementing band-pass filters involves the use of lumped LC components to produce classical filters based on the technique of low-pass to band-pass transformation. Several variations of topologies can be synthesized for producing desired band-pass filter responses. The shortcomings of such filters are numerous for purposes of processing broadband signals in the VHF and UHF frequency bands, the most serious of which is that the lumped components (particularly the coil inductors) are highly susceptible to parasitic effects at frequencies much above 100 MHz. Moreover, several stages of circuit components must be cascaded together to achieve the complexity of transfer function requisite for a high value of QL. Thus, such filters take up valuable space and make their cost of manufacture relatively high.
Another known technique for implementing filters employs helical resonators. Filters employing helical resonators are magnetically and/or capacitively coupled and are capable of producing a response with the high QL and low insertion loss requisite for many broadband signal-processing applications. They are not, however, suitable for frequencies much below 150 MHz, because very large inductor values would be required for the resonators below that frequency. Such inductors are impractical or impossible to construct. Moreover, even at higher frequencies they are rather large mechanical structures (they require shielding both for proper operation and to reduce susceptibility to RF noise), which makes them relatively expensive to manufacture (even in high volumes). They also are highly susceptible to environmental shock and drift, and they typically require an adjustment in value during the manufacturing process to make sure that they resonate accurately at the proper frequency.
Yet another known technique for building band-pass filters employs magnetically and/or capacitively-coupled dielectric resonators, implemented either as cylindrical coaxial transmission lines, or as printed strip transmission lines sandwiched in between two ground plane shields. These resonators are short-circuited transmission lines, and as such are exploited for their ability to resonate at a particular frequency as a function of their length relative to the wavelength of the transmitted input signal (the length of the line is typically λ/4 for the wavelength λ of the resonant frequency). Such resonators are capable of producing high QL values to achieve responses having the fractional bandwidth characteristic requisite for many broadband signal-processing applications (i.e. 1-2%). Because the trace length increases as the desired resonant frequency decreases, however, such resonators are not suitable for anything other than UHF (i.e. between about 400 MHz and several GHz). They become cost prohibitive for HF and VHF applications because the lengths of the transmission lines increase to a prohibitive size. Even at 1 to 2 GHz, these implementations require trace lengths on the order of about 2 to 1 inches respectively, which is still quite large and consumes significant area. Moreover, this would not scale well to manufacturing technologies of higher resolution (e.g. integrated circuits) because the length required to achieve one quarter of the wavelength is orders of magnitude too large for such technologies. Finally, such long quarter wavelength resonators are highly susceptible to transmitting and receiving noise.
Another well-known circuit topology for producing a band-pass filter response is that of the magnetically coupled, double-tuned resonant circuit. Band-pass filters so implemented are the least expensive to manufacture relative to the other various prior art techniques discussed herein (they can be manufactured for a few cents each). Implementations of such filters heretofore known have been unable to achieve the large QL values necessary to produce responses having small fractional bandwidths and low insertion loss requisite of many applications such as broadband signal processing (they have typically achieved no better than about 15% fractional bandwidth or greater). The reasons for their shortcomings in such applications will be apparent to those of skill in the art in view of the following discussion.
The generic topology of a series double-tuned circuit 10 is illustrated in FIG. 1a, and that of a parallel double-tuned circuit 100 is illustrated in FIG. 2b. The series double-tuned circuit has an input resonator circuit 12 that is magnetically coupled to an output resonator circuit 14. Likewise, the parallel double-tuned circuit 100 has an input resonator circuit 120 magnetically coupled to an output resonator circuit 140. The input resonators 12, 120 are coupled to an input source modeled by sources VS 18, 180 and associated source impedances RS 16 and 160 respectively. The output resonators 14, 140 are coupled to the output load impedance modeled by resistors RL 15, 150 respectively.
The input and output resonators 12, 14 of the series tuned circuit 10 are formed as a series connection between lumped series capacitors CS1 11 and CS2 13 respectively, and inductors L1 17 and L2 19 respectively. The two series tuned resonators 12, 14 and the two parallel tuned resonators 120, 140 are magnetically coupled as a function of the physical proximity between their inductors, whereby a mutual inductance M 21 is created between them. M=k√{square root over (L1·L2)}, where k is the coupling coefficient which has a value that is a function of the geometry of the inductive elements and their physical proximity to one another. Coupling coefficient k therefore reflects the percentage of the total potential mutual coupling between the two resonators. The closer in proximity the two inductors 17, 19 or 170, 190 are, the greater the value of k and therefore the greater the mutual inductance between the resonators; likewise, the further they are apart, the lower the degree of mutual inductance as reflected by the lower the value of k.
The parallel double-tuned circuit 100 is the theoretical dual of the series double-tuned circuit 10, and thus operates quite similarly. The resonators 120, 140 of the parallel tuned circuit 100 are formed as a parallel connection between lumped capacitors CP1 110 and CP2 130, and inductors L1 170 and L2 190 respectively. The parallel tuned resonators 120, 140 are also magnetically coupled as a function of the physical proximity between their inductors, whereby a mutual inductance M 210 is created between them. The mutual inductance of the parallel tuned circuit is given by the same equation, M=k√{square root over (L1·L2)}, with its value of k dictated by the same geometrical considerations as previously discussed.
FIG. 2 illustrates three typical responses of a double-tuned resonant circuit (either series or parallel), for different values of the coupling coefficient k. Response 22 is obtained when the two resonators of the circuit are critically coupled at the resonant frequency, which is the point at which the circuit exhibits an optimal combination of minimal insertion loss and average selectivity at the resonant frequency. Response 24 illustrates the response of the double-tuned circuits 10 and 100, when their respective input and output resonators are under-coupled. This occurs for values of k approaching zero, which can be accomplished by moving the resonators of the circuit further apart. When undercoupled, the value of the circuits' QL increases (the fractional bandwidth decreases) but the insertion loss also increases, which is not desirable. Response 26 occurs when the two inductors of the input and output resonators are so close together they become over-coupled (i.e. k approaches a value of 1). Response 26 is characterized by two maxima on either side of the resonant frequency, but the circuits exhibit their lowest QL value (and thus their largest fractional bandwidth). From these responses, it can be seen that there is a trade-off for double-tuned filter implementations, between the maximum attainable QL value and insertion loss. For a given frequency, this tradeoff is effected as a function of the mutual inductance M between the resonators of such filter implementations. Optimal coupling clearly occurs at or near the critical range, because it provides the best compromise between stop-band performance and insertion loss.
It is important to note that as frequency increases, the overall inductive coupling between the resonators increases. This is because the overall inductive coupling between the resonators is not only a function of the mutual inductance M (which is a function of the geometric properties and the proximity of the resonators), but is also a function of the inductive reactance, which is a direct function of frequency (i.e. w·M). Thus, as frequency increases for a given value of M, the inductive coupling between the resonators increases and the circuit eventually becomes over-coupled. To a certain point, one can compensate for this increase in coupling by simply increasing the spacing between the inductors, thereby lowering M by decreasing k. However, increasing the spacing at frequencies in the 1 GHz range and above becomes impracticable.
The QL for a series tuned circuit is roughly determined as the reactance X of the tuned circuit network at the resonant frequency (wo·L ), divided by the load or source impedance coupled to it. Thus, QL for the output resonator 14 is   ≅                              w          0                ·                  L          2                            R        L              .  For a given resonant frequency wo, one could increase the QL by increasing the value of L2. (Of course, to increase the overall QL for the series double-tuned resonator, one would do the same for the input resonator 12 by increasing the value of L1 as well). The problem with this approach is that there are practical limitations on the size of the inductors L1, L2 that can be manufactured and implemented at a reasonable cost. Moreover, as the values of L1, L2 are increased, the parasitic shunt capacitance associated with a lumped value inductor (typically a coil) degrades the frequency response of the filter at frequencies above 200 MHz. Finally, because the resonant frequency is determined by the equation       w    0    =      1                            L          2                ·                  C          S2                    (for the output resonator 14), the value of CS2 must be reduced commensurately to maintain the value of wo. There are also practical limitations on how small CS2 can be built accurately.
FIG. 3 illustrates the series double-tuned circuit 10 of FIG. 1 with values for k, CS1 11 and Cs2 13, and L1 17 and L2 19, designed to push the value of QL, while maintaining optimal coupling for the circuit at a resonant frequency of 400 MHz. FIGS. 4a and 4b show the simulated response for the circuit 30 having the indicated component values as shown in FIG. 3. The pairs of values across the bottom of FIGS. 4a and 4b indicate the frequency (in MHz) and attenuation (in dB) values for the points 1-4 as indicated on the response curve. The response as shown in the scale provided in FIG. 4a illustrates the unacceptable performance of the filter at high frequencies for television signal processing applications. The smaller scale provided by FIG. 4b shows the 3 dB fractional bandwidth to be about 16% (and thus the approximate value of QL is 6.25). As previously discussed, this is unacceptable for many broadband signal processing applications.
The QL for a parallel tuned circuit is roughly determined as the admittance of the network at the resonant frequency, multiplied by the load or source impedance coupled to it. Thus, QL for the parallel tuned output resonator 140 is ≡wo·CP2·RL. Thus, it can be seen that to increase QL for the parallel tuned output resonator, one could increase the value of CP2 and RL·RL can't be increased much above 100 ohms, as the signal would tend to be shunted to ground through parasitic shunt elements. Increasing CP2 requires that L2 be made very small. To manufacture lumped inductors on the order of 5 nH using known techniques with acceptable accuracy is very difficult, as such inductors are very sensitive to geometric variation, especially longitudinally. Furthermore, obtaining and maintaining proper coupling between such small coils on a repeatable basis is nearly impossible. The small coils require a small gap between them to maintain optimal coupling (typically at or near critical coupling), and the coupling coefficient is highly sensitive to dimensional variations in this small gap. Such component and dimensional variations cannot be tolerated when fractional bandwidths on the order of 1% are required.
FIG. 5 illustrates the parallel double-tuned circuit 100 of FIG. 1 with values for k, CP1 110 and CP2 130, and L1 170/L2 190, with an L to C ratio designed to push QL for the circuit with optimal coupling at a resonant frequency of 400 MHz. FIGS. 6a and 6b show the simulated response for the circuit 50 having the indicated component values as shown in FIG. 3. The pairs of values across the bottom of FIGS. 6a and 6b indicate the frequency (in MHz) and attenuation (in dB) values for the points 1-4 as indicated on the response curve. The response as shown in the scale provided in FIG. 6a illustrates the unacceptable performance of the filter in the stop-band, even though it operates more symmetrically at high frequencies relative to the series tuned circuit 30 of FIG. 3. Even though the coil values used in this example of the prior art are being pushed to the limit, the bandwidth of this filter is still not narrow enough for many applications. The smaller scale provided by FIG. 6b shows the 3 dB fractional bandwidth to be about 15.5% (and thus the approximate value of QL is 6.45. As previously discussed, this is unacceptable for many broadband signal processing applications that require fractional bandwidths of 1 to 2% (i.e. QL values in the 50 to 100 range).
Thus, those of skill in the art will recognize the need for band-pass filter circuits that provide characteristics required for many broadband signal processing applications over bandwidths spanning about 50 to 2000 MHz or greater. Those characteristics are namely high Qua values to provide high selectivity and therefore small fractional bandwidths, high attenuation in the stop-band, low insertion loss in the pass-band, and which can be manufactured as cheaply and repeatably as the tuned resonator circuits of the prior art.